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This paper is the final published version; however, page numbers will be inserted
when all the papers in the issue have been finalized. Thank you.
The Effect of Sustainability
Features on Mortgage Default
Prediction and Risk in
Multifamily Rental Housing
Author
Gary Pivo
Abstract
This study examines the relationship between transportation-, location-,
and affordability-related sustainability features and default risk in
multifamily housing. It finds that sustainability features can be used to
improve the prediction of mortgage default and reduce default risk. The
study uses 37,385 loans in the Fannie Mae multifamily portfolio at the
end of 2011:Q3. The results suggest two implications for practice. First,
certain aspects of sustainability can be fostered without increasing
default risk by adjusting conventional lending standards. Second, lenders
could improve their risk management practices by taking stock of
sustainability features when loans originate.
This study examines the relationship between sustainability features and mortgage
default risk in multifamily rental housing. The borrowers are multifamily rental
building owners with loans held by Fannie Mae. The sustainability features pertain
to the social and environmental performance of properties including affordability,
walkability, auto dependence, exposure to pollution, and proximity to protected
open space.
The results show that information on the sustainability of multifamily buildings
improves our ability to predict mortgage defaults. The results also show that loans
on properties with sustainability features have a much lower risk of default. For
example, defaults were 58% less likely for loans on properties in less autodependent locations, where 30% or more of the workers living there commute by
subway or elevated train. Similarly impressive findings were found for each of
the sustainability features examined in the study.
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Mortgage Default and Multifamily Housing
Mortgage loan defaults are a risk for multifamily lenders and investors. In a study
of 495 securitized multifamily mortgages originating between 1989 and 1995,
Archer, Elmer, Harrison, and Ling (2002) found a default rate of nearly 12%.
More recently, in the fourth quarter of 2011, the default rate for multifamily
mortgages held by depository institutions in the United States was 3.7% (Chandan,
2011).
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Previous studies show that the major risk factors for multifamily loan default are
cash flow and property value. Default risk increases if declining cash flow prevents
loan repayment or if falling property value produces negative net equity (Vandell,
1984, 1992; Titman and Torous, 1989; Kau, Keenan, Muller, and Epperson, 1990;
Vandell, Barnes, Hartzell, Kraft, and Wendt, 1993; Goldberg and Capone, 1998,
2002; Archer, Elmer, Harrison, and Ling, 2002). In these studies, cash flow and
equity are commonly measured in terms of debt service coverage ratio (DSCR),
or the ratio of income to required loan payments, and loan-to-value ratio (LTV),
or the ratio of loan amount to property value. A lower DSCR and a higher LTV,
both at origination and over the life of the loan, have been linked to greater default
risk.
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The Connection between Mortgage Default and
Sustainability
A growing number of econometric studies show that buildings with sustainability
features generate more cash flow and value. The value premium appears to come
from both the stronger cash flow and lower capitalization rates, suggesting that
more sustainable properties are favored in both the space and capital markets by
renters and investors. Stronger cash flow has also been tied to lower operating
expenses. Specific sustainability features linked to these effects include LEED
certification, ENERGY STAR labeling, historic preservation, design excellence,
proximity to open space, good transit service, walkability, revitalizing urban
location, and reduced exposure to pollution and natural hazards (Vandell and Lane,
1989; Harrison, Smersh, and Schwartz, 2001; McGreal, Webb, Adair, and Berry,
2006; Simons and Saginor, 2006; Miller, Spivey, and Florance, 2008; Eichholtz,
Kok, and Quigley, 2009; Pivo and Fisher, 2010, 2011). Perhaps this should be
unsurprising. After all, sustainability features promote qualities long associated
with higher property value including health, safety, operating efficiency, occupant
amenities, and accessibility.
If more sustainable buildings have better cash flow and value, then they should
also exhibit lower default risk because, as noted above, default risk is inversely
related to cash flow and value. However, adding information on sustainability
features to the loan origination process would only be helpful if their impact on
cash flow and value was not already fully accounted for in that process. If the
financial benefits of sustainability were already fully reflected in the cash flow
and value projections made at loan origination, then rational lenders may have
already increased the size of the loans or reduced loan interest rates for the more
sustainable properties (Grovenstein, Harding, Sirmans, Thebpanya, and Turnbull,
2005). The higher loan amounts or lower interest rates for the more sustainable
properties would in turn have increased their LTV or lowered their DSCR,
resulting in a probability of default more like that found in more conventional
properties. That is to say, the effect of the sustainability variables would have
already been fully endogenous to the loan origination process (Archer, Elmer,
Harrison, and Ling, 2002). That would have caused the ex post default risk for
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The Effect of Sustainability Features
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the more sustainable properties to end up being similar to the risk for the
conventional ones. In that case, adding the sustainability features to a default
prediction model, which already includes the original LTV and DSCR, would not
improve the ability of the model to predict default because the information carried
by the sustainability regressors would already be included in the LTV and DSCR.
However, if the financial benefits of sustainability had not been fully accounted
for when the loans were originated, but instead future cash flows and values for
more sustainable properties were expected to be closer to those of conventional
properties than they actually turned out to be, then as any unrecognized financial
benefits from the sustainability features materialized post-origination, the average
post-origination DSCR would turn out to be higher and the average postorigination LTV would turn out to be lower for the more sustainable properties
than for the conventional ones. This would produce a lower default rate for the
more sustainable properties compared to the conventional ones, because there
would be a lower risk of negative cash flow or a lower risk of negative equity.
This is not to say that lenders would have completely ignored sustainability
features at loan origination. Indeed, some of them, such as being in a transitoriented location, are commonly recognized by lenders as locational advantages.
But even if some of the sustainability features were previously recognized as
advantages by lenders, as long as their full effect on cash flow, value, and default
risk were not fully reflected in the original loan terms, the more sustainable
properties would have a lower post-origination default rate than the more
conventional ones.
In a modeling context, if the financial benefits of sustainability were not
completely reflected in the original DSCR and LTV, then adding information on
sustainability features to a default prediction model could significantly improve
the accuracy of that model. Put another way, if sustainability features help buffer
properties from losing cash flow and value in the face of energy shocks, recessions,
competition, or other events that can push cash flow and value into the default
‘‘danger zone’’ (Bradley, Cutts, and Follain, 2001), then knowing that a property
is more or less sustainable should help lenders mitigate default risk.
These expectations led to Hypotheses 1 and 2.
Hypothesis 1: If certain transportation-, location-, and housing-related
sustainability features are added to a model of default risk,
the accuracy of the model will improve.
This is based on the expectation that most, if not all, of the impact that
sustainability features have on future cash flow and value was unanticipated when
multifamily loans were originated. Even though some advantages of the features
may have been considered by underwriters, this hypothesis proposes that their
positive effect on cash flow or value was not fully accounted for in the original
loan terms.
Hypothesis 2: Sustainability features will be associated with a lower risk
of default, ceteris paribus.
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This should be the case because prior research shows that sustainability features
tend to be associated with increased cash flow and value, which are in turn related
to lower default risk.
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Methods
Logistic Regression Model
A logistic regression model was used to test the hypotheses. This model has been
used in several prior studies to estimate the effects of explanatory variables on
the probability of mortgage default (Vandell, Barnes, Hartzell, Kraft, and Wendt,
1993; Goldberg and Capone, 1998, 2002; Archer, Elmer, Harrison, and Ling,
2002, Rauterkus, Thrall, and Hangen, 2010). A primer on logistic regression and
its alternatives for studying default risk is given in the Appendix.
The data on individual mortgages used to build the model was provided by Fannie
Mae and then combined by the author with data from other sources in order to
measure sustainability and control variables. The Fannie Mae data included
information on every loan in its multifamily portfolio at the end of 2011:Q3,
making the study cross-sectional rather than longitudinal. The cross-sectional
design raises some concern about the external validity of the findings (i.e., how
far the findings can be generalized beyond the study sample) because the
relationships between the regressors and default risk could change over time. For
example, proximity to transit could reduce default rates by a greater amount when
gas prices are peaking and demand is higher for apartments near public transit.
Unfortunately, longitudinal data were unavailable for this study. It would be useful
to confirm the results reported here in a follow-up study using longitudinal data.
Another external validity issue comes from the fact that the Fannie Mae mortgage
pool had an average default rate that was about one-fourth the rate found for
mortgages held by depository institutions. It would be important to know whether
the effects found in this study apply to those mortgages as well.
In the present work, each loan was treated as a separate case or observation. For
each case, data were available on the loan age, type, terms, and lender, on various
financial, physical, and locational attributes of the collateral property, and on the
number of days the loan was delinquent, if any. More details on these variables
and those from other sources are given below.
Following Archer, Elmer, Harrison, and Ling (2002), cases in the Fannie Mae
database with extreme values on certain variables were excluded from the study
in order to filter out possible measurement error. The extreme value filters ensured
that all the cases used had an original note interest rate greater than the 10-year
constant maturity risk-free rate at their origination date, an original LTV ratio of
100% or less, an original DSCR greater than 0.9 and less than 5.0, and an original
note interest rate greater than 3% and less than 15%. After these filters were
applied, 37,385 loans remained in the sample out of the 42,474 cases. The sample
included mortgages with fixed and adjustable rates and with a wide variety of
seasoning, originating anywhere from September, 1971 to September, 2011.
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The variables evaluated in the models are described in the next section. Exhibit 1
gives their definitions and summary statistics.
Variables
DEFAULT was a binary variable indicating whether or not a loan was in default
as of 2011:Q3. Loans were classified as in default if they were delinquent on their
payments by 90 days or more as of 2011:Q3.
Seven sustainability variables were analyzed. Sustainability is a multi-dimensional
construct with multiple distinct but related dimensions treated as a single
theoretical concept. As such, the variables used in this study could not capture
every dimension normally used to assess building sustainability (Pivo, 2008). Key
omissions due to data limitations included operational energy and water efficiency.
It would be useful to test the effect of these and other sustainability metrics on
mortgage outcomes in future studies. If they affect cash flow and value, they are
likely to affect default risk as well.
For some of the sustainability variables, a dummy that indicated whether their
value fell above or below a cut-point produced a better result in the models than
a continuous variable. This is common when a change in the dependent variable
associated with a one-unit change in the independent variable is nonlinear and
there is a suspected or assumed threshold effect (Williams, Mandrekar, Mandrekar,
Cha, and Furth, 2006). Where nonlinearity was suspected, possible cut-points were
examined by categorizing the relevant continuous sustainability variable into
quantiles (e.g., quartiles or deciles) and comparing the default rates for each group.
Default rates significantly higher for all mortgages above or below a certain
quantile indicated a discontinuity and suggested a likely cut-point where a
threshold effect may occur. The cut-point was then used to create a new dummy
variable for testing in the model. This procedure was used iteratively to find the
‘‘optimal’’ cut-point which produced a dichotomous variable that was most useful
in predicting default. In a practical setting, cut-points can be more useful than
continuous indicators because they allow a simple risk classification into ‘‘high’’
and ‘‘low’’ and communicate clearly the threshold above (or below) which default
risk will be consistently above (or below) average.
Three variables were used to capture the nature of the journey to work by residents
living in the census tract where each property was located. These variables address
the air, water, and wildlife issues linked to commuting and related social issues
including traffic accidents, physical activity, and social interaction. COMMUTE
TIME was the average commute time in minutes for people 16 years of age and
older living in the tract who worked outside the home. SUBWAY30 indicated
whether a property was in a tract where at least 30% of the workers take a subway
or elevated train to work. The 30% cut-point was selected using the ‘‘optimal cutpoint’’ method described above. PCTWALK indicated the percentage of people in
the tract who walk to work. All commuting data were from the 2000 U.S. Census.
Newer data were unavailable at the time of the study. It is unlikely, however, that
changes in commuting patterns over the past decade were sufficient to significantly
alter the results.
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Pivo
E x h i b i t 1 u Definitions and Summary Statistics for Variables in Final Models (n 5 37,385)
Variable
Dependent Variable
DEFAULT
Definition
Binary variable indicating whether loan
was (1) or was not (0) in default.
Default was defined as .90 days
delinquent as of 2011:Q3.
Sustainability Variables
COMMUTE TIME
Mean commute time in 2000 for
residents in the census tract (minutes).
SUBWAY30
In census tract where at least 30% of
workers use a subway or elevated train
for work (1 5 yes, 0 5 no).
PCTWALK
Percent of people in census tract that
walked to work in 2000.
RETAIL16
Sixteen or more retail establishments in
census block group (1 5 yes, 0 5 no).
AFFORDABLE
Meets FNMA affordable housing
standards (1 5 yes, 0 5 no).
FREEWAY1000FT
Within 1,000 feet of an interstate
freeway (1 5 yes, 0 5 no).
PROTECTED1MILE
Within 1 mile of a protected area (1 5
yes, 0 5 no).
Control Variables
OLTV
ODSCR
LOAN AGE
MONTHS
LOAN SIZE GP
ARM FLAG
NOCONCERNS
BUILT YR
TOT UNTS CNT
PRINCIPAL CITY
URB RUR
MEDHHINC000
PROP CRIME MIL
Loan-to-value ratio at origination.
Debt service coverage ratio at
origination.
Number of months since loan
origination.
Original loan size; ordinal variable (1
# $3MM, 2 5 $3–5MM, 3 5 $5–
25MM, 4 $ $25MM).
Dummy for adjustable-rate mortgage
(1 5 yes, 0 5 no).
Dummy indicating absence (1) or
presence (0) of concerns about
physical condition at origination.
The year the property was built.
Total housing units in the property.
Dummy for whether or not located in
U.S. Census Principal City (1 5 yes,
0 5 no).
Ordinal variable indicating whether
property is in Principal Urban Center,
Metro City, Urban Outskirts, Suburban
Periphery, Small Town or Rural
location.
Median household income in census
tract in 2000 (000 dollars).
Annual number of property crimes per
million persons in the city.
Min.
0
2.10
Max.
1
75.50
Mean
Std. Dev.
0.01
0.09
26.72
6.72
0
1
0.08
0.27
0
100
4.92
7.40
0
1
0.40
0.49
0
1
0.10
0.30
0
1
0.40
0.49
0
1
0.71
0.45
0.59
0.90
100
5.0
61.30
1.52
16.29
0.549
0.00
468.00
73.15
52.91
1
4
1.70
0.97
0
1
0.31
0.46
0
1
0.28
0.40
1800
2
0
2011
3284
1
1967.83
94.65
0.60
26.25
125.05
0.49
1
7
1.92
1.16
0.0
200.00
42.70
16.94
0.0
2849.85
407.48
165.31
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E x h i b i t 1 u (continued)
Definitions and Summary Statistics for Variables in Final Models (n 5 37,385)
Variable
Definition
US PRICE CHANGE
Percent change in NCREIF U.S.
Apartment Index from quarter loan
originated to 2011:Q3.
Dummy for New England region.
Dummy for Mid-Atlantic region.
Dummy for East North Central region.
Dummy for West North Central region.
Dummy for South Atlantic region.
Dummy for East South Central region.
Dummy for West South Central region.
Dummy for Mountain region.
Dummy for Pacific region.
Average apartment price change in
percent from 2005:Q3 to 2011:Q3 in
percent in the MSA.
Average apartment occupancy rate in
percent from 2005:Q3 to 2011:Q3 in
percent in the MSA.
Dummy for in one of 25 most populous
U.S. cities (1 5 yes, 0 5 no).
Dummy for in New York City (1 5 yes,
0 5 no).
Dummy for in Washington, DC (1 5
yes, 0 5 no).
NEWENGLAND
MIDATLANTIC
ENCENT
WNCENT
SOATLANTIC
ESOCENTRAL
WSOCENT
MTN
PACIFIC
AVG PRICE 6
AVG OCC 6
TOP25CITY
NYC
DC
Min.
Max.
Mean
Std. Dev.
213.54
137.89
16.26
27.22
0
0
0
0
0
0
0
0
0
250.30
1
1
1
1
1
1
1
1
1
20.79
0.03
0.14
0.08
0.04
0.09
0.02
0.08
0.05
0.47
21.33
0.17
0.35
0.26
0.19
0.29
0.14
0.27
0.22
0.50
3.51
100
91.04
3.66
0
1
0.23
0.42
0
1
0.03
0.16
0
1
0.06
0.08
33.43
RETAIL16 captured walkability where the apartment buildings were located or the
degree to which the area within walking distance of a property encourages walking
from the property to other destinations. Walkability has been linked to various
social and environmental benefits and increases with the number of desired
destinations within walking distance of a property (Pivo and Fisher, 2011; Federal
Highway Administration, 2012). RETAIL16 was a dummy indicating whether the
property was in a census block group with at least 16 retail establishments in 2011
and also was selected using the ‘‘optimal cut-point’’ method. The data were
collected from Nielsen Claritas, which estimated the number of establishments in
2011 based on the 2007 U.S. Economic Census. The author is currently
completing work on a follow-up study that examines the relationship between
Walk Score—a widely available walkability metric—and multifamily mortgage
risk.
AFFORDABLE indicated whether or not the loan was part of the Fannie Mae
Targeted Affordable Segment, which focuses on financing properties with rent
subsidies or income restrictions. Family well-being can be in jeopardy if too much
of a household’s budget is required for housing, leaving too little money for food,
health care, childcare or other essentials (Bratt, 2002).
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FREEWAY1000FT indicated whether a property was located within 1,000 feet of
a freeway. There is growing evidence that living close to a freeway increases risk
for autism, cancers, and respiratory disease (Gauderman et al., 2007; Volk, HertzPicciotto, Delwiche, Lurmann, and McConnell, 2011; Office of Health Hazard
Assessment, 2012; Cakmak, Mahmud, Grgicak-Mannion, and Dales, 2012). Data
on highway locations was obtained from the 2011 National Transportation Atlas
Database.
PROTECTED1MILE indicated whether a property was located within a mile of a
Protected Area according to the U.S. Protected Area Database. It includes public
lands at all government levels held for conservation and voluntarily provided
privately protected areas. Protected open space helps sustain resource-based
industry, recreation, wildlife, watersheds, and other ecosystem services such as
greenhouse gas absorption and heat island mitigation. Access to parks and
recreation has also been linked to lower childhood obesity and other social benefits
(Wolch et al., 2011).
In this study, the expectation was that if certain sustainability features were related
to default risk, it is because they affect cash flow and/or value to a degree
unaccounted for in the DSCR or LTV ratio at loan origination. However, it could
also be true that the sustainability features are correlated with other factors that
affect financial outcomes and default risk, such as other loan, property,
neighborhood, or macroeconomic variables, raising questions about whether
sustainability is a proxy for these other drivers of cash flow and value. Therefore,
to separate the effects of sustainability features on default risk from these other
factors, several control variables, suggested by prior research, were used in the
models. The controls fall into four groups including loan, property, neighborhood,
and economic characteristics.
OLTV and ODSCR measure the LTV and debt service coverage ratios at loan
origination. Higher OLTV and lower ODSCR were expected to be associated with
greater default risk. LOAN SIZE GP was an ordinal variable for the loan amount
at origination. Esaki, L’Heureux, and Snyderman (1999) found that smaller
commercial loans had lower default rates. ARM FLAG was a dummy indicating
whether the loan is adjustable or fixed. LOAN AGE MONTHS was the number
of months from the loan origination date to the observation date. Previous
researchers have shown that default risk declines with age, though the pattern is
nonlinear, increasing rapidly in the first few years and then declining (Snyderman,
1991; Esaki, L’Heureux, and Snyderman, 1999; Archer, Elmer, Harrison, and Ling,
2002). The same pattern was observed in this study sample. Linearity is not a
requirement of the logistic regression model and it was unnecessary to transform
LOAN AGE MONTHS to obtain significant results. However, some non-linearity
in the logit was detected for LOAN AGE MONTHS using the Box-Tidwell
transformation (Menard, 1995), so transformations of LOAN AGE MONTHS
were tried but they did not improve the results.
NO CONCERNS was a dummy indicating whether there were no substantial
concerns about the property condition at the time of loan origination. This should
reduce default risk by decreasing the need to divert cash flow to deferred
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maintenance. BUILT YR was the year the property was built. Archer, Elmer,
Harrison, and Ling (2002) found that default rates increased with building age, so
BUILT YR was expected to be inversely related to default risk, although in some
areas historic buildings may be prevalent, which could influence how age relates
to risk.
TOT UNTS CNT was the total number of units in the property. Smaller properties
have been reported to experience more financial distress (Bradley, Cutts, and
Follain, 2000). Archer, Elmer, Harrison, and Ling (2002), however, found that size
was unrelated to default, although their univariate analysis showed that smaller
properties had less risk, contrary to Bradley, Cutts, and Follain (2000). So the
expected effect in this study was ambiguous.
Four control variables were created to control for geographical effects at the city
and neighborhood level. Archer, Elmer, Harrison, and Ling (2002) found
geographical effects to be one of the most important dimensions for predicting
multifamily mortgage default. PRINCIPAL CITY indicated whether the property
was located in a Principal City, defined by the U.S. Census as the largest
incorporated or census designated place in a core-based statistical area. Its purpose
was to control for whether or not a property was centrally located in a metro- or
micropolitan area because many central areas have outperformed suburban
locations over the past decade and several sustainability features, such as
walkability, are more common in central cities. Properties in Principal Cities were
expected to have lower default risk. URB RUR was also used to measure regional
centrality. It was based on the 11 Urbanization Summary Groups defined in the
ESRI Tapestry Segmentation system, which groups locations along an urban-rural
continuum from ‘‘Principal Urban Centers’’ to ‘‘Small Towns and Rural’’ places.
MEDHHINC000 was the median household income in the census tract from the
2000 census. Higher income was expected to be linked with lower default rates.
PROP CRIME MIL was the annual number of property crimes per million
persons at the city scale, reported by the U.S. Department of Justice. Higher crime
was expected to increase default risk.
Regional and national variables were used to control for differences in the
economic context experienced by properties since loan origination. Dummies were
created for the nine census divisions. Vandell, Barnes, Hartzell, Kraft, and Wendt
(1993) used a similar variable. Other variables were tested but found to be
insignificant. They included state, metropolitan area, and city location. Additional
variables designed to capture regional economic effects were whether the property
was in one of the 25 largest cities (TOP25CITY), dummies for whether the
property was located in New York City (NYC) or Washington, DC (DC), and
changes in vacancy rates and prices in the metro area in the most recent six-year
period. USPRICE CHANGE was a national indicator that captured the percentage
change in the National Council of Real Estate Investment Fiduciaries (NCREIF)
U.S. Apartment Index that occurred from the time the loan was originated to the
observation date (2011:Q3). AVG PRICE 6 and AVG OCC 6 were computed
using the NCREIF Apartment Index for metro areas. They described the average
increase in apartment prices and the average occupancy rate in the metro area for
each property over the last six years prior to the study observation date. Prior
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researchers have used updates of LTV and DSCR over time to predict default on
the theory that negative equity or cash flow will trigger default. Both are affected
by the property’s net operating income, which is in turn affected by vacancy rates
and rental price indices. Therefore, changes in vacancy rates and rental price
indices at the metro scale can be used to capture changes in market conditions
that strengthen or weaken mortgages over time (Goldberg and Capone, 1998,
2002).
Lenders consider borrower characteristics to be crucial in predicting default rates.
Relevant variables include borrower character, experience, financial strength, and
credit history. In their ‘‘simple model of default probability,’’ Archer, Elmer,
Harrison, and Ling (2002) theorized that losses from loans depend on the risk
characteristics of the borrower, among other things, though such variables were
not included in their models. Vandell, Barnes, Hartzell, Kraft, and Wendt (1993)
used borrower type (individual, partnership, corporation, other) in their analysis
of commercial mortgage defaults, as did Ciochetti, Deng, Gao, and Yao (2003),
who expected individuals to represent a lower risk to lenders, although neither
study found these variables to be significant. Unfortunately, due to privacy
concerns, data on borrowers were unavailable for this study. It is likely, however,
that lenders adjusted the original loan terms based in part on their assessment of
borrower characteristics. Therefore, the LTV, DSCR, and ARM FLAG variables
may serve as proxies for borrower characteristics. It is inappropriate to make
assumptions, however, about the effects of omitting variables in logistic regression.
It is known that omitting relevant variables introduces bias into linear regression,
but less is known about how it may bias logistic regression (Dietrich, 2003). One
study showed that omitted orthogonal variables (i.e., variables that are uncorrelated
with other independent variables) can depress the estimated parameters of the
remaining regressors toward zero (Cramer, 2007). That would make the findings
about sustainability in this study appear to be weaker than they actually are. It
would be helpful to include borrower characteristics in future work building on
the present study.
Correlation among the independent variables is indicative of collinearity.
Collinearity can create modeling problems including insignificant variables,
unreasonably high coefficients, and incorrect coefficient signs (e.g., negatives that
should be positive). Collinearity will not affect the accuracy of a model as a whole,
but it can produce incorrect results for individual variables, which makes it more
of a concern for Hypothesis 2 than Hypothesis 1. Tolerance statistics, which check
for a relationship between each independent variable and all other independent
variables, were used as an initial check and raised no concerns (Menard, 1995).
A pairwise correlation matrix among the independent variables, however, did
indicate possible issues. LOAN AGE MONTHS and USPRICE CHANGE were
moderately correlated (0.737), as were TOT UNTS CNT and LOAN SIZE GP
(0.662), both of which make logical sense. SUBWAY30 was also correlated with
MIDATLANTIC (0.684) and NYC (0.601). Correlations at this level do not
automatically mean there will be collinearity issues, but they do raise the need
for further tests, which were done and are reported below.
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Results
Exhibit 2 gives the statistics for the three final models produced for the study.
The first model predicts DEFAULT only using conventional explanatory variables
E x h i b i t 2 u Logistic Regression Results for DEFAULT
Model 1:
Model 2:
Model 3:
Without Sustainability
With Sustainability
Significant Variables Only
b (sig.)
b (sig.)
Exp(b)
b (sig.)
Exp(b)
1.045
0.355
0.996
1.596
0.043 (.000)
21.043(.001)
20.004 (.020)
0.477 (.000)
1.044
0.352
0.996
1.611
Exp(b)
Loan
OLTV
0.041 (.000) 1.042
ODSCR
20.868 (.003) 0.420
LOAN AGE MONTHS 20.005 (.002) 0.995
ARM FLAG
0.578 (.000) 1.782
0.044
21.037
20.004
0.468
Property
NOCONCERNS
BUILT YR
TOT UNTS CNT
20.902 (.000) 0.406
20.015 (.000) 0.985
20.004 (.000) 0.996
20.820 (.000) 0.440
20.016 (.000) 0.985
20.004 (.000) 0.996
20.827 (.000) 0.437
20.016 (.000) 0.984
20.004 (.000) 0.996
Neighborhood
PRINCIPAL CITY
URB RUR
MEDHHINC000
PROP CRIME MIL
0.145
0.041
20.028
0.001
0.285
0.020
20.033
0.001
20.035 (.000) 0.966
0.001(.000) 1.001
Economy
TOP25CITY
DC
REGION
AVG PRICE 6
20.358 (.032)
21.158 (.115)
unreported
0.004 (.790)
(.297)
(.481)
(.000)
(.001)
1.156
0.960
0.973
1.001
(.057)
(.745)
(.000)
(.000)
1.330
0.980
0.968
1.001
0.699
20.564 (.002) 0.569
20.419 (.011) 0.658
0.314
21.420 (.056) 0.242
21.247 (.091) 0.287
unreported unreported
unreported unreported
unreported
1.004
0.005 (.742) 1.005
Sustainability
COMMUTE TIME
SUBWAY30
PCTWALK
RETAIL16
AFFORDABLE
FREEWAY1000FT
PROTECTED1MILE
Constant
(.000)
(.001)
(.019)
(.001)
0.041
20.821
20.031
20.417
20.959
0.455
20.401
24.620 (.000) 4.926E10
(.000)
(.014)
(.008)
(.002)
(.000)
(.044)
(.009)
1.042
0.440
0.969
0.659
0.383
1.576
0.669
25.841 (.000) 1.670E11
0.037
20.878
20.031
20.421
20.964
0.464
20.393
(.000)
(.008)
(.009)
(.002)
(.000)
(.040)
(.010)
1.037
0.416
0.969
0.656
0.381
1.590
0.675
25.492 (.000) 1.178E11
Notes: In all models, n 5 37,385. In Model 1, chi-square 5 549.54 (.000), 22 log-likelihood 5
3,097.149, Nagelkerke R2 5 .157, and under ROC curve 5 0.829. In Model 2, chi-square 5 625.55
(.000), 22 log-likelihood 5 3,019.951, Nagelkerke R2 5 .179, and under ROC curve 5 0.841. In Model
3, chi-square 5 621.54 (.000), 22 log-likelihood 5 3,023.967, Nagelkerke R2 5 .178, and under ROC
curve 5 0.841
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unrelated to sustainability. The second model repeats the first but adds the
sustainability variables. The third model is a reduced version of the second. It
drops insignificant variables to produce a more parsimonious model in order to
achieve the best fit with the fewest parameters. Using irrelevant variables increases
the standard error of the parameter estimates and reduces significance (Menard,
1995). Insignificant variables were kept in the second model so their effect on the
sustainability variables could be considered.
Some variables were excluded from the three final models due to collinearity
issues. LOAN AGE was insignificant and had the wrong sign when it was included
in the models with USPRICE CHANGE. This was corrected when LOAN AGE
was used without USPRICE CHANGE. LOAN AGE was kept instead
of US PRICE CHANGE because it captured the information included in
USPRICE CHANGE (since they were correlated), and because it captured the
effect of other forces that may have affected DEFAULT due to the seasoning of
the loan and the market conditions when and since the loan entered the market.
TOT UNTS CNT was insignificant when included with LOAN SIZE GP;
however both were significant on their own. TOT UNTS CNT was used in the
final models because it had more informational content than LOAN SIZE GP,
which was only ordinal rather than continuous.
The coefficient for SUBWAY30 was inflated when MIDATLANTIC and NYC were
in the model, so both were excluded, which produced more conservative results
(smaller effects) for SUBWAY30 in both cases. NYC was reintroduced in a
robustness check, which is discussed below.
Since collinearity tends to produce unreasonably high regression coefficients, a
rough indication of remaining collinearity in the models would be if any of the
unstandardized coefficients (b) were greater than 2 (Menard, 1995). This was not
the case, indicating the steps taken to reduce collinearity were sufficiently
effective.
In the final models, all the variables had the expected signs except for URB RUR;
however its results were insignificant. Also, larger properties had smaller default
rates, supporting the findings by Bradley, Cutts, and Follain (2000).
Goodness-of-Fit with and without Sustainability
The first hypothesis was that if certain sustainability features are added to a model
of default risk, the accuracy of the model will improve. This hypothesis was tested
by comparing the goodness-of-fit of models with and without sustainability
features included. Goodness-of-fit refers to how well all the explanatory variables
in a logistic regression model, taken together, predict the dependent variable.
Goodness-of-fit statistics are reported in the notes for Exhibit 2. For all of the
statistics except 22 log-likelihood, a higher value indicates a better fitting model.
All four statistics show there was less discrepancy between the observed values
for DEFAULT and the values produced by the model when sustainability features
were included. That supports the acceptance of Hypothesis 1.
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The model chi-square measures the total reduction for all the cases in default
prediction errors that occurs when the independent variables are in the model,
compared to when they are not. Comparing the model chi-squares across the
models in Exhibit 2 indicates that the models with the sustainability features
predicted default more accurately than the model without them. This is indicated
by a chi-square of 550 for Model 1 versus 626 and 622 for Models 2 and 3,
respectively.
The 22 log-likelihood statistic is similar to the model chi-square since it is based
on the total error made by the model in predicting default for all the cases
combined. But 22 log-likelihood measures the total error made by the model with
the independent variables included rather than the difference between the error
with and without the independent variables. That is, it measures how poorly a
model fits the data with all the independent variables in the equation. That is why
a better model has a smaller 22 log-likelihood. Here again, comparing across the
models in Exhibit 2, the results show that the models with sustainability variables
more accurately predicted default than the model without them, as indicated by
22 log-likelihood values of 3,020 for Model 1 versus 3,024 and 3,097 for Models
2 and 3.
The Nagelkerke R-Square is a ‘‘pseudo R-square’’ that can be computed in logistic
regression analysis. Pseudo R-squares are not analogous to the R-square in linear
regression and are easily misinterpreted by readers familiar with linear regression
models, according to Hosmer and Lemeshow (2000). For that reason, they
recommend against reporting them. The Nagelkerke R-square is a measure of
improvement from the null model to the fitted model (i.e., the improvement in
each model produced by adding the independent variables). It is most useful for
comparing multiple models predicting the same outcome with the same dataset,
as in the present case. When used that way, the models with the higher R-squares
are the ones that better predict the outcome. As Exhibit 2 shows, the models with
sustainability features included had higher Nagelkerke R-squares (.178 and .179
vs. .157).
Goodness-of-fit was also tested using the area under the receiver operating
characteristic (ROC) curve. This test measures the model’s ability to discriminate
between loans that do and do not default and is the likelihood that a loan that
defaults will have a higher predicted probability than a loan that does not. If the
result is equal to 0.5, the model is no better than flipping a coin. In the present
study, ROCs exceeded 0.8. Values at this level indicate excellent discrimination
according to Hosmer and Lemeshow (2000). In other words, the models did an
excellent job distinguishing between loans that will and will not default. Here
again, the models with sustainability features did a better job than the model
without (0.841 for both models with sustainability vs. 0.829 for the model
without).
The Hosmer–Lemeshow test is another commonly recommended statistical test
for goodness-of-fit in logistic regression models. However, its assumption that the
expected frequencies are large was violated because default was a relatively rare
event in this study, so its results would be invalid in the present case (Hosmer
and Lemeshow, 2000).
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According to all four goodness-of-fit measures, the results support the first
hypothesis that if certain sustainability features are added to a model of default
risk, the accuracy of the model improves.
Interpretation of Sustainability Coefficients
The second hypothesis was that sustainability features will be associated with a
lower risk of default. This hypothesis was tested by examining and interpreting
the regression coefficients in the reduced model (Model 3). According to the
significance tests (‘‘sig.’’ in Exhibit 2), all of the sustainability features were
significantly related to default risk. This means it is highly improbable that the
sustainability features would be so strongly related to default in a model with this
sample size if there actually were no relationships.
The size and direction of the relationships are indicated by the unstandardized
coefficients (b). In Models 2 and 3, b gives the change in the risk of default
associated with a one-unit change in the sustainability variables, while the control
variables are held constant. If b is positive, then default risk increases with each
one-unit increase in the sustainability variable. For example, in Model 3, a b of
0.041 for COMMUTE TIME indicates that the risk of default increases as the
average commute time increases in the area where the property is located. If b is
negative, then default risk decreases with each one-unit increase in the
sustainability variable. For example, in Model 3, a b of 20.878 for SUBWAY30
indicates that the risk of default decreases when a property is located where 30%
or more of the people commute to work by subway or elevated train. And since
these findings were estimated when the control variables were also in the model,
we can say they are true regardless of neighborhood income (MEDHHINC000),
whether or not the loan is adjustable (ARM FLAG), the debt service coverage
ratio at origination (ODSCR), etc.
Together, the significance tests and unstandardized coefficients in Models 2 and
3 indicate that when the sustainability features studied here are present, there is
less risk of default, all else being equal. Note, however, that for some of the
sustainability variables, a larger raw score indicates the property is less sustainable.
That is the case for COMMUTE TIME and FREEWAY1000FT. For these variables,
a positive b means that a lower value (which indicates less sustainability), such
as a longer commute time, is associated with less default risk. For the other
variables, a negative b means that a higher value (which indicates more
sustainability), such as more walking to work, is associated with less default risk.
The unstandardized coefficients can be used to obtain estimated odds ratios by
exponentiating the coefficients (i.e., computing its base e anti-log). An odds ratio
is the odds of an outcome in one group (e.g., the default rate for properties near
a protected area) divided by the odds of an outcome in another group (e.g., the
default rate for properties not near a protected area). It is analogous to relative
risk (Grimes and Schulz, 2008). The odds ratio associated with each independent
variable is given as Exp(b) in Exhibit 2. As explained by Menard (1995), the
odds ratio is the number by which we would multiply the odds of default for each
one-unit increase in the independent variable. An Exp(b) greater than 1 indicates
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E x h i b i t 3 u Summary of Sustainability Effects on Default Risk in Multifamily Mortgages
Effect on Relative
Risk of Default
Variable
Definition
COMMUTE TIME
Per 1 minute increase in the commute time to work.
SUBWAY30
Where $ 30% commute by subway or elevated.
PCTWALK
Per 1-unit increase in the percent who walk to work.
RETAIL16
Where there are 16 or more retail establishments in the block group.
34.4% less
AFFORDABLE
When property meets FNMA definition for affordable housing.
61.9% less
FREEWAY1000FT
Where property is located within 1,000 feet of a freeway corridor.
59.0% more
PROTECTED1MILE
Where property is located with 1 mile of protected open space.
32.5% less
3.7% more
58.4% less
3.1% less
that the odds of default increase when the independent variable increases and an
Exp(b) less than 1 indicates that the odds of default decrease when the
independent variable increases. For example, a one-unit increase in COMMUTE
TIME (i.e., a one-minute increase, according to the definition column in Exhibit
1) results in a 3.7% increase in the odds of default (the odds of default are
multiplied by 1.037). Similarly, a one-unit increase in SUBWAY30 results in a
58.4% decrease in the odds of default (the odds of DEFAULT are multiplied by
0.584, which is 0.416 less than 1). For a dummy variable that can only be scored
as 0 or 1, a one-unit increase is equivalent to referring to all cases where the
dummy variable has a score of 1 or Yes. So, for example, for SUBWAY30, if we
say that a one-unit increase decreases the odds of default by 58.4%, we are saying
that when SUBWAY30 is scored 1 (i.e., when a property is located in a location
where 30% or more of the people commute by subway or elevated to work), the
odds of default are 58.4% lower than in cases where the property is not located
in such a location and SUBWAY30 is scored 0.
Odd ratios can also be interpreted as relative risk when the outcome occurs less
than 10% of the time, which is the case for DEFAULT in the study sample
(Hosmer and Lemeshow, 2000). Relative risk is the ratio of the probability of an
event occurring in a group with and without a certain characteristic. We can say,
for example, that in locations where commute time is 28 minutes (or about one
minute above average), multifamily mortgages are 3.7% more likely to default
than in locations with a 27-minute commute time. Similarly, in locations where
30% or more residents take a subway or elevated train to work, owners are 58%
less likely to default in comparison to locations where fewer than 30% commute
by subway or elevated. And, as noted above, the reductions in risk associated with
the each of the sustainability features are unrelated to differences in regional
location, neighborhood income, and the other control variables included in the
models.
Exhibit 3 summarizes the effects of a one-unit change in the sustainability
variables on default risk in relative risk terms. In every case, the effects are large,
indicating that these sustainability features have a very significant effect on default
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risk, independent of other factors commonly used to predict default. In addition,
the direction of each relationship indicates that in all cases more sustainability is
related to less default risk. These findings confirm Hypothesis 2 that sustainability
features are associated with a lower risk of default.
When dealing with continuous variables, such as COMMUTE TIME and
PCTWALK, a one-unit change is not always interesting. For example, a one-minute
increase in commuting or a 1% increase in the percentage of people who walk to
work may be too small to be considered important. Hosmer and Lemeshow (2000,
p. 63) show that as in the case of a one-unit increase, the effect from a multi-unit
change in an independent variable on the odds of default can be determined from
an estimated odds ratio. In the case of a multi-unit change, the odds ratio is
estimated by exponentiating the product of the unstandardized coefficient (b) for
a given variable times the number of units of change. If, for example, one were
interested in how a 10-minute increase in COMMUTE TIME affected the odds of
default, the odds ratio would be computed by exponentiating the product of 10 3
b for COMMUTE TIME. Applying this method using the coefficients from Model
3 (Exhibit 2), we find that for every 10-minute increase in the mean commute
time for residents in a census tract, the risk of default increases by 45%. Similarly,
for every five-unit increase in the percentage of people in a tract who walk to
work, the risk of default decreases by 15%.
As discussed above, NYC was excluded from the models. This was because
SUBWAY30 was inflated with NYC in the model due to collinearity issues.
However, it was important to know if the effects of SUBWAY30 were due to its
association with NYC. To answer that question, Model 3 was rerun using the
33,733 cases that were not located in NYC. The unstandardized coefficient for
SUBWAY30 (b) was 21.062 (0.003) and the Exp(b) was 0.356. Compared to the
results in Exhibit 2, this indicates that the effect of SUBWAY30 outside of NYC
was even stronger. When cases in New York City were excluded from the sample,
the relative risk of default was 64.4% less for properties located where at least
30% of the tract residents commuted by subway or elevated, compared to 58.4%
less when cases in New York City were included in the sample. This indicates
that the effects of SUBWAY30 on default were not because a disproportionate share
of the cases in subway-oriented locations were in New York City.
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Discussion
The findings support the hypotheses. When certain transportation-, location-, and
affordability-related sustainability features are included in a default probability
model for multifamily housing, the model predicts default more accurately. Also,
properties with the sustainable features studied are much less likely to default.
These findings suggest two important implications for practice: one pertaining to
sustainability and the other to risk management.
First, certain aspects of sustainability can be fostered without increasing default
risk by adjusting conventional lending standards for properties with the
sustainability features studied here to achieve the same risk of default associated
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with less sustainable properties. For example, in the study sample, the mean OLTV
and ODSCR were 0.61 and 1.52, respectively. However, according to Model 3, if
a property is located in a subway-oriented census tract (where at least 30% of the
people commute by subway or elevated train), then the OLTV could have been
raised to nearly 0.75 and the ODSCR could have been lowered to 1.28 (which
maintains the normal ratio between the two found in the sample) and the
probability of default would have remained virtually equal to that found for
properties not located near subway stations, all else being equal. According to the
model, the extra risk produced by a higher OLTV and lower ODSCR would be
offset by the lower risk produced by locating in a more sustainable location,
leaving the total risk unchanged. Similar results can be produced with various
other combinations of the studied sustainability features and conventional lending
standards. Of course, lenders have programmatic constraints that set maximums
for the OLTV and minimums for the ODSCR. Those constraints establish practical
limits on how far lenders could go in adjusting for sustainability features unless
they are willing to make exceptions to the programmatic constraints for that
purpose.
If higher LTV ratios at origination could be obtained by borrowers for more
sustainable properties, the borrowers would achieve a higher return on equity as
long as positive leverage is possible (i.e., when the cost of debt financing is lower
than the overall return generated by the property return on asset). Ceteris paribus,
this should cause investors to prefer more sustainable investments, increase capital
flow to more sustainable buildings, and foster a transition to more sustainable
cities.
The second implication of the findings is that lenders could improve their risk
management practices by taking stock of whether a property has certain
sustainability features when loans are originated. All the features studied here are
based on existing federal datasets provided by the Census Bureau and other
agencies. So it would be relatively easy to build an online address-based lookup
tool that any lender can use to obtain certain sustainability information on a given
property. In addition, recommended adjustments to OLTV and ODSCR ratios could
be made available through a second online tool based on coefficients found in this
study and confirmed by additional research. The results clearly show that
traditional lending ratios have not fully recognized the presence or absence of
certain sustainability features (by recognizing their effect on capitalization rates,
values, or cash flows). The most common result is that these ratios have been
based on an underestimation of the actual risk of default for properties without
those sustainability features. This is because the ‘‘normal’’ rate of default expected
for all properties is derived from the experience with more and less sustainable
properties combined, without the effect of sustainability being recognized. In this
situation, less sustainable properties, according to the findings in this study, should
have a rate of risk higher than the norm. There is more risk associated with less
sustainable properties (and less risk with more sustainable properties) than is being
accounted for in traditional lending ratios. If better information could be made
available on the size of these effects and on how lending ratios could be adjusted
to offset the effects produced by the presence or absence of sustainability features,
the risk of portfolios could be more effectively managed.
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Unfortunately, this study is limited to those sustainability features for which data
could be obtained. It is likely, however, that other sustainability features that were
not studied here also have beneficial effects on default risk. The most likely
examples pertain to energy efficiency and green building certification because prior
studies show they affect cash flow and value. Other sustainability features that
could reduce default risk include rental unit flexibility, urban centrality, noise
mitigation, water efficiency, childcare services, and school quality. This is
expected because of their likely ‘‘materiality’’ to financial performance, rather than
their positive effect on the public good (Pivo, 2008). Further work on whether
these features do or do not affect default risk would be most useful, but it will
have to await the development of better databases to account for them.
Other fruitful avenues for further research include repeating this study using other
modeling methods (e.g., longitudinal hazard models) and data sets on higher risk
mortgages. It would also be useful to conduct similar studies on other property
types, including single-family homes and other commercial property types. And
work should begin on a practical tool that helps lenders adjust conventional
lending ratios based on sustainability information without increasing normal risk
levels.
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Conclusion
Perhaps the most important point of this study is that sustainability is just as much
an issue with material consequence for investors as for those interested in social
and environmental well-being. Pivo and McNamara (2005) wrote about the
common ground emerging between real estate investing and sustainability stating:
‘‘It is probably apparent to anyone who thoughtfully considers real estate that it
can both contribute to and be affected by many of the social and environmental
issues that face the world’s societies. Until recently, however, most real estate
investors would likely have said that while they are sympathetic, such issues
are...not of direct concern to their investment practices. But today, a new view is
emerging...that various social and environmental issues can have significant
material consequences for their investment portfolios.’’
Sustainability is financially consequential for property investors. Multifamily
lenders can mitigate risk by gearing their portfolios toward more sustainable
properties. Moreover, and for society this may be even more important, lenders
can offer more favorable terms to more sustainable properties without increasing
default risk, or as Benjamin Franklin once said, they can ‘‘do well by doing good.’’
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Appendix
Logistic Regression and Alternatives
Logistic regression is a statistical method for predicting the value of a bivariate
dependent variable (Menard, 1995). A bivariate variable is one with two possible
values, such as pass/fail, or in the present study, default/no default. The value of
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the dependent variable predicted by a logistic regression model is the probability
that a case will fall into the higher of the two categories of the dependent variable,
which normally indicates the event occurred, given the values for the case on the
independent variables. In other words, it is the probability that an event will occur
under various conditions characterized by the independent variables. The predicted
value of the dependent variable is based on observed relationships between it and
the independent variable or variables used in the study.
Logistic regression models are typically used to determine whether the
classification of cases into one of the two categories of the dependent variable
can be predicted better from information on the independent variables than if the
cases were randomly classified into the categories. ‘‘Goodness-of-fit’’ refers to
how well all the explanatory variables in a logistic regression model, taken
together, predict the dependent variable. So, in terms of logistic regression, the
first hypothesis in this paper is that a logistic regression model for default will
have a better goodness-of-fit if sustainability features are included along with other
more conventional explanatory variables in the regression equation.
The estimated parameters of a logistic regression equation can be interpreted as
the change in the dependent variable that can be expected from a one-unit change
in the dependent variable, holding other dependent variables constant. So again,
looking at the second hypothesis in this paper in terms of logistic regression
analysis, the expectation is that sustainability features will have estimated
parameters that show they reduce the probability of default by a significant
amount.
The most common alternative to the logistic regression model in mortgage default
research is the proportional hazard model. Hazard models explain the time that
passes before some event occurs in terms of covariates associated with that
quantity of time. They have been used to estimate the probability that a mortgage
with certain characteristics will default in a given period if there has been no
default up until that period (Vandell, Barnes, Hartzell, Kraft, and Wendt, 1993;
Ciochetti, Deng, Gao, and Yao, 2002; Teo, 2004). Other methods for predicting
default also have been explored including neural networks (Episcopos, Pericli, and
Hu, 1998) and a maximum entropy approach (Stokes and Gloy, 2007).
A common view of the hazard model is that it is less sensitive to bias from
database censuring than logistic regression. Censoring occurs when cases are
removed from the database prior to observation (e.g., when a loan is paid off or
foreclosed and sold prior to observation) or when the event of interest happens
after observation occurs (e.g., when a loan defaults after the study observation
date). However, as pointed out by Archer, Elmer, Harrison, and Ling (2002), bias
is only an issue in logistic regression when the explanatory variables have a
different effect on the censored and uncensored cases. In the present study, there
is no reason to expect that sustainability features affected the odds of default
differently in censored and uncensored cases. Hazard models also require a time
series dataset that reports the occurrence of defaults over time and such a dataset
was unavailable at the start of the present study. One effort to predict mortgage
pre-payment using both approaches found that the logistic regression model made
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better predictions (Pericli, Hu, and Masri, 1996), while in another study on
insolvency among insurers, the two models produced equally accurate predictions
(Lee and Urrutia, 1996). So, while it would be interesting to repeat this study
using a hazard model, there is no a priori reason to assume that the logistic
regression method used here produced results that are inferior to those that would
have come from another method.
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Characteristics and Financial Risk among Multifamily Properties. Journal of Housing
Economics, 2001, 10, 482–506.
Bratt, R.G. Housing and Family Well-Being. Housing Studies, 2002, 17:1, 13–26.
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